Average Error: 0.3 → 0.3
Time: 11.6s
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
\[\frac{1 - \log \left(e^{\tan x}\right) \cdot \tan x}{1 + \tan x \cdot \tan x}\]

Error

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Results

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Derivation

  1. Initial program 0.3

    \[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
  2. Initial simplification0.3

    \[\leadsto \frac{1 - \tan x \cdot \tan x}{\tan x \cdot \tan x + 1}\]
  3. Using strategy rm
  4. Applied add-log-exp1.1

    \[\leadsto \frac{1 - \color{blue}{\log \left(e^{\tan x \cdot \tan x}\right)}}{\tan x \cdot \tan x + 1}\]
  5. Using strategy rm
  6. Applied exp-prod1.1

    \[\leadsto \frac{1 - \log \color{blue}{\left({\left(e^{\tan x}\right)}^{\left(\tan x\right)}\right)}}{\tan x \cdot \tan x + 1}\]
  7. Applied log-pow0.3

    \[\leadsto \frac{1 - \color{blue}{\tan x \cdot \log \left(e^{\tan x}\right)}}{\tan x \cdot \tan x + 1}\]
  8. Final simplification0.3

    \[\leadsto \frac{1 - \log \left(e^{\tan x}\right) \cdot \tan x}{1 + \tan x \cdot \tan x}\]

Runtime

Time bar (total: 11.6s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.30.30.10.30%
herbie shell --seed 2018339 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))